The proposal to clear the city of fighters with thel Nusra Front, made by UN Special Envoy for Syria Staffan de Mistura, was intended as a means to ease hostilities in the besieged city.
"I heard his statement concerning only Nusra. For God's sake, if al-Nusra leaves with weapons toward Idlib, where its main forces are based, we are ready to support this approach for the sake of Aleppo and will be ready to urge the Syrian government to agree," Lavrov said in an interview with Russia's Channel One.
Opposition fighters remaining in Aleppo after the UN special envoy's plan is enacted should be clearly separated from the militant group, he added.
It's unclear exactly how de Mistura's plan would be carried out or whether the Nusra Front -- now known as Jabhat Fatah al Sham -- would sign up to any such deal.
US Secretary of State John Kerry meanwhile blasted Russia and the Syrian regime for what he said was yet another attack on a hospital in Aleppo overnight that killed 20 people and injured 100.
Speaking in Washington on Friday alongside French Foreign Minister Jean-Marc Ayrault, Kerry said Russia and the Syrian regime "owe the world more than an explanation about why they keep hitting hospitals and medical facilities and children and women."
Those responsible should be held accountable for these actions, Kerry said, saying they were "way beyond -- years beyond -- the accidental."
Kerry said the two would discuss "how best to deliver the strongest message possible" about the "siege of innocent people" in Aleppo.
Ayrault called Aleppo a "human tragedy" and warned that if nothing was done, Aleppo could be destroyed by the end of the year.
UN Security Council meets
Ayrault's meeting with Kerry follows a trip a day earlier to Moscow, where he met with Lavrov.
France on Thursday submitted a draft resolution to the UN Security Council calling for an end to hostilities in Aleppo and access for humanitarian aid.
Lavrov said Russia was "ready to work on this text" as long as it didn't contradict any other UN resolutions or US-Russia ceasefire agreements.
Members of the United Nations Security Council are meeting Friday to discuss the crisis in Aleppo.
According to Sputnik News, participants in the closed-door session are expected to discuss the proposal by de Mistura.
At his press briefing in Geneva, de Mistura asked the Nusra fighters if they "are going to stay there [and] keep hostage [the civilians in the] city, because 1,000 of you are deciding the destiny of the 275,000 civilians."
"If you did decide to leave, in dignity, and with your weapons, to Idlib, or anywhere you wanted to go, I personally, I am ready physically to accompany you," he said.
De Mistura also appealed directly Thursday to Russia and the Syrian regime to bring an end to the fighting in Aleppo, as he warned that the war-torn Syrian city could be destroyed within months
"Look me in the eyes, are you really ready to continue this level of fighting, using those type of weapons, and destroy eastern Aleppo with 275,000 people, for the sake of killing 900 al-Nusra fighters?" he asked.